... {a1,a2,a 3 ,a4} can be written in theformσ =1 234 21 43 ,indicating that a1went to a2, a2 to a1, a 3 to a4, and a4 to a 3 .Ifwealwayschoosethetoprowtobe1 234 then, to prescribe ... ω2, ω 3 , and ω5. Each ofthese paths has the same probability p2q.Thusb (3, p,2)=3p2q. Considering allpossible numbers of successes we haveb (3, p,0) = q 3 ,b (3, p,1)=3pq2,b (3, p,2)=3p2q,b (3, p ,3) ... +1possibilities. Hence, the total number of sequences with no duplications is 36 5 36 4 · 36 3 · · (36 5 −r +1).Thus, assuming that each sequence is equally likely,pr= 36 5 36 4 · · (36 5 − r +1) 36 5r.We denote...